If they went third party, I fully anticipate my interest in Nintendo products would drop below that crucial threshold where I'm actually willing to pay them any money.
I don't own the competing platforms, and I'm not sure I would just because Nintendo games were available on them. It's not like I'm hurrying out to get a smart phone so I can play Pokémon Rumble/Pokémon Go/Miitomo/Fire Emblem Heroes/Super Mario RUN.
Before anyone says that these are completely different games, I am willing to argue that Nintendo's console offerings would also have to be completely different in order to be viable on competing platforms.